NCERT solutions for class 6 mathematics -Exercise Solutions

Chapter 05-Understanding Elementary Shapes-Exercise Solutions

NCERT Book Page Number-88
Q.1. What is the disadvantage in comparing line segments by mere observation?
Answer: By mere observation, we cannot be absolutely sure about the judgement. When we compare two line segments of almost same lengths, we cannot be sure about the line segment of greater length. Therefore, it is not an appropriate method to compare line segments having a slight difference between their lengths. This is the disadvantage in comparing line segments by mere observation.
Q.2. Why is it better to use a divider than a ruler, while measuring the length of a line segment?
Answer: It is better to use a divider than a ruler because while using a ruler, positioning error may occur due to the incorrect positioning of the eye.
Q.3. Draw any line segment, say $\overline AB$. Take any point C lying in between A and B. Measure the lengths of AB, BC and AC. Is AB = AC + CB?
[Note: If A, B, C are any three points on a line such that AC + CB = AB, then we can be sure that C lies between A and B]
Answer:
It is given that point C is lying somewhere in between A and B. Therefore, all these points are lying on the same line segment$\overline AB$. Hence, for every situation in which point C is lying in between A and B, it may be said that AB = AC + CB.
For example,
$\overline AB$ is a line segment of 6 cm and C is a point between A and B, such that it is 2 cm away from point B. We can find that the measure of line segment $\overline AC$ comes to 4 cm.
Hence, relation AB = AC + CB is verified.
NCERT Book Page Number-89

Q.4. If A, B, C are three points on a line such that AB = 5 cm, BC = 3 cm and AC = 8 cm, which one of them lies between the other two?
Answer: Given that,
AB = 5 cm
BC = 3 cm
AC = 8 cm
It can be observed that AC = AB + BC
Clearly, point B is lying between A and C.

Q.5. Verify, whether D is the mid point of $\overline AG$ .


Answer:
From the given figure, it can be observed that
$\overline AD$= 4 − 1 = 3 units
$\overline DG$= 7 − 4 = 3 units
$\overline AG$ = 7 − 1 = 6 units
Clearly, D is the mid-point of AG.
Q.6. If B is the mid point of $\overline AC$ and C is the mid point of$\overline BD$, where A, B, C, D lie on a straight line, say why AB = CD?
Answer:


Since B is the mid-point of AC,
AB = BC (1)
Since C is the mid-point of BD,
BC = CD (2)
From equation (1) and (2), we may find that
AB = CD
NCERT Book Page Number-91
Q.1. What fraction of a clock wise revolution does the hour hand of a clock turn through when it goes from
(a) 3 to 9
(b) 4 to 7
(c) 7 to 10
(d) 12 to 9
(e) 1 to 10
(f) 6 to 3
Answer: We may observe that in 1 complete clockwise revolution, the hour hand will rotate by 360º.
(a) When the hour hand goes from 3 to 9 clockwise, it will rotate by 2 right angles or 180º.
Fraction = $\frac{{180}^{o}}{{360}^{o}}$
$=\frac{1}{2}$


(b) When the hour hand goes from 4 to 7 clockwise, it will rotate by 1 right angle or 90º.
Fraction = $\frac{{90}^{o}}{{360}^{o}}$
$=\frac{1}{4}$


(c) When the hour hand goes from 7 to 10 clockwise, it will rotate by 1 right angle or 90º.
Fraction = $\frac{{90}^{o}}{{360}^{o}}$
$=\frac{1}{4}$


(d) When the hour hand goes from 12 to 9 clockwise, it will rotate by 3 right angles or 270º.
Fraction = $\frac{{270}^{o}}{{360}^{o}}$
$=\frac{3}{4}$


(e) When the hour hand goes from 1 to 10 clockwise, it will rotate by 3 right angles or $270^{0}$.
Fraction = $\frac{{270}^{o}}{{360}^{o}}$
$=\frac{3}{4}$


(f) When the hour hand goes from 6 to 3 clockwise, it will rotate by 3 right angles or $270^{0}$.
Fraction = $\frac{{270}^{o}}{{360}^{o}}$
$=\frac{3}{4}$


Q.2. Where will the hand of a clock stop if it
(a) Starts at 12 and makes $\frac{1}{2}$ of a revolution, clockwise?
(b) Starts at 2 and makes$\frac{1}{2}$ of a revolution, clockwise?
(c) Starts at 5 and makes $\frac{1}{4}$ of a revolution, clockwise?
(d) Starts at 5 and makes $\frac{3}{4}$ of a revolution, clockwise?
Answer:
In 1 complete clockwise revolution, the hand of a clock will rotate by $360^{0}$.
(a) If the hand of the clock starts at 12 and makes $\frac{1}{2}$ of a revolution clockwise, then it will rotate by 180º and hence, it will stop at 6.


(b) If the hand of the clock starts at 2 and makes $\frac{1}{2}$ of a revolution clockwise, then it will rotate by 180º and hence, it will stop at 8.


(c) If the hand of the clock starts at 5 and makes $\frac{1}{4}$ of a revolution clockwise, then it will rotate by $90^{0}$ and hence, it will stop at 8.


(d) If the hand of the clock starts at 5 and makes $\frac{3}{4}$ of a revolution clockwise, then it will rotate by $270^{0}$ and hence, it will stop at 2.


Q.3. Which direction will you face if you start facing


(a) East and make $\frac{1}{2}$ of a revolution clockwise?
(b) East and make1$\frac{1}{2}$ of a revolution clockwise?
(c) West and make $\frac{3}{4}$ of a revolution anti-clockwise?
(d) South and make one full revolution?
(Should we specify clockwise or anti-clockwise for this last question? Why not? )
Answer:
If we revolve one complete round in either clockwise or anti-clockwise direction, then we will revolve by $360^{0}$ and the two adjacent directions will be at $90^{0}$ or $\frac{1}{4}$ of a complete revolution away from each other.
(a) If we start facing East and make $\frac{1}{2}$ of a revolution clockwise, then we will face the West direction.


(b) If we start facing East and make 1$\frac{1}{2}$ of a revolution clockwise, then we will face the West direction.


(c) If we start facing West and make $\frac{3}{4}$ of a revolution anti-clockwise, then we will face the North direction.


(d) If we start facing South and make a full revolution, then we will again
face the South direction.


In case of revolving by 1 complete round, the direction in which we are revolving does not matter. In both cases, clockwise or anti-clockwise, we will be back at our initial position.

Q.4. What part of a revolution have you turned through if you stand facing
(a) East and turn clock wise to face north?
(b) South and turn clockwise to face east?
(c) West and turn clockwise to face east?
Answer:
If we revolve one complete round in either clockwise or anti-clockwise direction, then we will revolve by 360º and the two adjacent directions will be at 90º or $\frac{1}{4}$ of a complete revolution away from each other.
(a) If we start facing East and turn clockwise to face North, then we have to make $\frac{3}{4}$ of a revolution.


(b) If we start facing South and turn clockwise to face east, then we have to make$\frac{3}{4}$ of a revolution.


(c) If we start facing West and turn clockwise to face East, then we have to make $\frac{1}{2}$ of a revolution.


Q.5. Find the number of right angles turned through by the hour hand of a clock when it goes from
(a) 3 to 6 (b) 2 to 8 (c) 5 to 11
(d) 10 to 1 (e) 12 to 9 (f) 12 to 6
Answer:
The hour hand of a clock revolves by $360^{0}$ or 4 right angles in 1 complete round.
(a) The hour hand of a clock revolves by $90^{0}$ or 1 right angle when it goes from 3 to 6.


(b) The hour hand of a clock revolves by $180^{0}$ or 2 right angles when it goes from 2 to 8.


(c) The hour hand of a clock revolves by $180^{0}$ or 2 right angles when it goes from 5 to 11.


(d) The hour hand of a clock revolves by $90^{0}$ or 1 right angle when it goes from 10 to 1.


(e) The hour hand of a clock revolves by $270^{0}$ or 3 right angles when it goes from 12 to 9.


(f) The hour hand of a clock revolves by $180^{0}$ or 2 right angles when it goes from 12 to 6.